Our aim in this paper is to further explore when states in two copies of a holographic system have a bulk wormhole description. We will argue that as we move away from the TFD, it is natural to consider mixed states on \(\mathcal {H}_L \otimes \mathcal {H}_R\) .Mixed states generalising TFD were considered from a different perspective in [1]}. A similar density matrix to the ones we consider was also recently considered for different purposes in [2]}. For small departures from TFD, this is motivated by noting that the geometry obtained in [3]} or [4]} doesn't depend on the details of the operators considered, so the bulk geometry can be related to a density matrix obtained by averaging over the operators. Density matrices are usually written as a sum over states in \(\mathcal {H}_L \otimes \mathcal {H}_R\) ; we refer to this as the state frame of the density matrix. The density matrices corresponding to different bulk geometries should have disjoint support in the space of quantum states. Different states drawn from the same density matrix have the same gravitational profile, but differ in microscopic data.
